This is the idea for an app I have wanted to build for many years. This would be a database of personal beliefs (also known as a "Propositional Knowledge Base"), connected via logical arguments of various kinds: deductive, inferential and Bayesian. Any new facts you learn should update the certainties of the involved beliefs and propagate that through the graph. You could build a social network around it, giving all users a chance to learn from each other's worldview. This would also help one detect inconsistencies and contradictions. The challenge here is to allow local contradictions without blowing up the system as Principle of Explosion implies.
- Probabilistic Graphical Models_ course on Stanford
- Automated reasoning software tools like Samiam
- Sentential Decision Diagram